OP have been to the South Island several times I'd also agree you should avoid Tekapo.
A few years ago I stayed at the Hermitage at Mt Cook and found they have regular stargazing at the local airstrip a few km from the hotel, out in the valley well away from all lights - and they have a 12" dob you can use. Or BYO gear, up to you.
IMHO it was the darkest site I've ever observed from - the gegenshein can be seen and that's really rare these days. Also possible to get a photo from a compact camera, for example
https://www.dpreview.com/galleries/7...06188/p1010566
Pretty much anywhere in central Otago will do too, but don't think about heading for peaks, you'll have to make do with being in a valley, unless your mad enough to backpack your gear to key summit on the routeburn track.